The use of the binomial distribution in establishing an association between high-risk donors and transfusion-associated AIDS.

In the first seven cases of transfusion-associated acquired immunodeficiency syndrome (TA-AIDS) with completion of blood donor investigations, there was identification of at least one person (a high-risk donor--HRD) in each donor set who might have transmitted the disease. Using three definitions of an HRD, we estimated the prevalence of HRDs in the overall donor population and used the binomial distribution to calculate the probabilities of finding at least the observed numbers of donor sets with one or more HRDs. These probabilities--0.028, 0.007 and 0.014, respectively--allowed us to reject the null hypothesis that the number of cases of TA-AIDS exposed to an HRD was not greater than that expected by chance, based on the total number of donors to which each case was exposed and the estimated proportion of HRDs in the overall donor population. We concluded that there was a statistically significant association between HRDs and TA-AIDS.